Best Known (166, 201, s)-Nets in Base 3
(166, 201, 896)-Net over F3 — Constructive and digital
Digital (166, 201, 896)-net over F3, using
- 3 times m-reduction [i] based on digital (166, 204, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 51, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- trace code for nets [i] based on digital (13, 51, 224)-net over F81, using
(166, 201, 5097)-Net over F3 — Digital
Digital (166, 201, 5097)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3201, 5097, F3, 35) (dual of [5097, 4896, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(3201, 6617, F3, 35) (dual of [6617, 6416, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(27) [i] based on
- linear OA(3185, 6561, F3, 35) (dual of [6561, 6376, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3145, 6561, F3, 28) (dual of [6561, 6416, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(316, 56, F3, 6) (dual of [56, 40, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(316, 80, F3, 6) (dual of [80, 64, 7]-code), using
- the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(316, 80, F3, 6) (dual of [80, 64, 7]-code), using
- construction X applied to Ce(34) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(3201, 6617, F3, 35) (dual of [6617, 6416, 36]-code), using
(166, 201, 1472656)-Net in Base 3 — Upper bound on s
There is no (166, 201, 1472657)-net in base 3, because
- 1 times m-reduction [i] would yield (166, 200, 1472657)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 265614 288895 055735 584377 533930 459644 133897 517180 425009 807511 564150 067544 896189 380584 806234 952931 > 3200 [i]